Alright Tetrahedron

Geometry Level 5

In a tetrahedron $ABCD,$ the lengths of $AB,$ $AC,$ and $BD$ are $6,$ $10,$ and $14$ respectively. The distance between the midpoints $M$ of $AB$ and $N$ of $CD$ is $4.$ The line $AB$ is perpendicular to $AC,$ $BD,$ and $MN.$ The volume of $ABCD$ can be written as $a\sqrt{b},$ where $a$ and $b$ are positive integers, and $b$ is not divisible by the square of a prime number. What is the value of $a+b$ ?

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Alright Tetrahedron

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 8 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.